Strong unique continuation for higher order elliptic equations with Gevrey coefficients (Q665973)

The authors address the strong unique continuation problem for higher order elliptic partial differential equations in 2D with Gevrey coefficients. They provide a quantitative estimate of unique continuation (observability estimate) and prove that the solutions satisfy the strong unique continuation property for ranges of the Gevrey exponent strictly including non-analytic Gevrey classes. As an application, they obtain a new upper bound on the Hausdorff length of the nodal sets of solutions with a polynomial dependence on the coefficients.